基于预计算权重与阈值的神经网络5输入XOR参数调整方案

我尝试用C++实现一个采用阶跃激活函数的阈值逻辑网络，以计算5输入XOR函数，且不进行任何训练。已有可正常运行的3输入XOR代码，但扩展到5输入后无法得到正确输出。原有的网络权重矩阵仅适用于3输入XOR，对5输入无效。

3输入XOR可运行代码 #

#include <iostream>  
using namespace std;  

int main() {  
    const int layer1 = 3;  
    const int layer2 = 4;  

    int weights_l1l2[layer2][layer1] = {  
        {2, -1, -1},   
        {-1, 2, -1},
        {-1, -1, 2},
        {1, 1, 1},   
    };  

    int threshold_l2[layer2] = {2, 2, 2, 3};  

    int weightsl2l3[layer2] = {1, 1, 1, 1};  

    int threshold_l3 = 1;   

    for (int i = 0; i < (1 << layer1); ++i) {   
        int x[layer1];  
        for (int j = 0; j < layer1; ++j) {  
            x[j] = (i >> (layer1 - 1 - j)) & 1;   
        }  

        for (int j = 0; j < layer1; ++j) {  
            cout << x[j];  
        }  

        int y[layer2];  
        for (int j = 0; j < layer2; ++j) {  
            int sum = 0;  
            for (int k = 0; k < layer1; ++k) {  
                sum += x[k] * weights_l1l2[j][k];  
            }  
            y[j] = sum >= threshold_l2[j] ? 1 : 0; // Activation function  
        }  

        int output = 0;  
        int sum = 0;  
        for (int j = 0; j < layer2; ++j) {  
            sum += y[j] * weightsl2l3[j];  
        }  
        output = sum >= threshold_l3 ? 1 : 0; // Activation function  

        cout << "\t" << output << endl;  
    }  

    return 0;  
}  

5输入XOR当前代码（无法正确输出） #

#include <iostream>  
using namespace std;  

int main() {  
    const int layer1 = 5;  
    const int layer2 = 6; // Number of Rows in the Weight Matrix 

    int weights_l1l2[layer2][layer1] = {  
        {4, -1, -1, -1, -1},   
        {-1, 4, -1, -1, -1},
        {-1, -1, 4, -1, -1},
        {-1, -1, -1, 4, -1},
        {-1, -1, -1, -1, 4},
        {1, 1, 1, 1, 1}
    };  

    int threshold_l2[layer2] = {2, 2, 2, 2, 2, 5}; // Might need adjustment 

    int weightsl2l3[layer2] = {1, 1, 1, 1, 1, 1};  

    int threshold_l3 = 1;   

    for (int i = 0; i < (1 << layer1); ++i){   
        int x[layer1];  
        for (int j = 0; j < layer1; ++j) {  
            x[j] = (i >> (layer1 - 1 - j)) & 1;   
        }  

        for (int j = 0; j < layer1; ++j) {  
            cout << x[j];  
        }  

        int y[layer2];  
        for (int j = 0; j < layer2; ++j) {  
            int sum = 0;  
            for (int k = 0; k < layer1; ++k) {  
                sum += x[k] * weights_l1l2[j][k];  
            }  
            y[j] = sum >= threshold_l2[j] ? 1 : 0; // Activation function  
        }  

        int output = 0;  
        int sum = 0;  
        for (int j = 0; j < layer2; ++j) {  
            sum += y[j] * weightsl2l3[j];  
        }  
        output = sum >= threshold_l3 ? 1 : 0; // Activation function  

        cout << "\t" << output << endl;  
    }  

    return 0;  
}  

疑问 #

• 应如何调整权重与阈值，使网络对所有5位输入输出正确的XOR结果？
• 是否存在确定整数权重的已知方法或公式？

内容的提问来源于stack exchange，提问作者Josh C.